距离分离系综密度泛函理论中激发态的外推与鬼相互作用修正相结合
Combining extrapolation with ghost interaction correction in range-separated ensemble density functional theory for excited states
摘要：
Savin [J. Chem. Phys. 140，18 A509（2014）]的外推技术最初应用于距离分离基态密度泛函哈密顿量，在这项工作中适用于激发态的重影相互作用校正（GIC）距离分离系综密度泛函理论（eDFT）。虽然标准的外推依赖于能量衰减为$μ^{-2}$在大范围分离参数$μ$限制，我们分析表明，（近似）距离分离GIC系综能量收敛更迅速（$μ^{-3}$）对他们的纯波函数理论值（$μ\rightarrow+\infty$限制），因此需要不同的外推校正。这种校正的目的是进一步改善收敛，并因此获得有限（并且实际上相对较小）$μ$值的更精确的激发能量。作为一个概念的证明，我们应用外推法，他和小分子系统（即H $_{2}$，HeH $^{+}$和LiH），从而考虑不同类型的激发，如里德伯，电荷转移和双激发。势能曲线的前三个和四个单重$Σ^+$激发能在HeH $^{+}$和H $_{2}$，分别研究了特别侧重于避免交叉后者。最后，作为一个角度，讨论了从系综能量中提取单个状态能量的范围分离的eDFT的上下文中。
英文摘要：
The extrapolation technique of Savin [J. Chem. Phys. 140, 18A509 (2014)], which was initially applied to range-separated ground-state-density-functional Hamiltonians, is adapted in this work to ghost-interaction-corrected (GIC) range-separated ensemble density-functional theory (eDFT) for excited states. While standard extrapolations rely on energies that decay as $μ^{-2}$ in the large range-separation-parameter $μ$ limit, we show analytically that (approximate) range-separated GIC ensemble energies converge more rapidly (as $μ^{-3}$) towards their pure wavefunction theory values ($μ\rightarrow+\infty$ limit), thus requiring a different extrapolation correction. The purpose of such a correction is to further improve on the convergence and, consequently, to obtain more accurate excitation energies for a finite (and, in practice, relatively small) $μ$ value. As a proof of concept, we apply the extrapolation method to He and small molecular systems (viz. H$_{2}$, HeH$^{+}$ and LiH), thus considering different types of excitations like Rydberg, charge transfer and double excitations. Potential energy profiles of the first three and four singlet $Σ^+$ excitation energies in HeH$^{+}$ and H$_{2}$, respectively, are studied with a particular focus on avoided crossings for the latter. Finally, the extraction of individual state energies from the ensemble energy is discussed in the context of range-separated eDFT, as a perspective.
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